Frequency control array MIMO radar parameter estimation method based on Bayesian tensor

Abstract

The invention provides a frequency control array MIMO radar parameter estimation method based on a Bayesian tensor. Aiming at a target parameter estimation problem in a frequency control array MIMO radar with array mutual coupling, the method comprises the following steps of: firstly, constructing a frequency control array MIMO radar receiving signal containing unknown mutual coupling, DOA (Direction of Arrival) and distance information into a third-order complex value tensor model; secondly, designing a selection matrix by utilizing the property of array mutual coupling to eliminate the array mutual coupling influence in a third-order complex value tensor receiving signal; then, optimizing the tensor model through real valuation and compression operation to obtain a three-order real value compression tensor so as to reduce the calculation complexity of tensor decomposition; finally, three factor matrixes are estimated through Bayesian tensor decomposition, and then the target number, DOA and distance information are obtained. Therefore, the method provided by the invention can effectively eliminate the mutual coupling influence of the array, realizes high-precision parameter estimation under the condition that the target number is known and unknown, and has remarkable advantages in the actual application of the radar.

Description

Technical Field

[0001] The present invention relates to the technical field of radar parameter estimation, and particularly to a method for estimating the parameters of a frequency-controlled array MIMO radar based on Bayesian tensors. Background Art

[0002] In detection systems such as radar, sonar, and remote sensing, target parameter estimation is a core technology for obtaining key information such as the target angle and distance. In recent years, the frequency-controlled array multiple-input multiple-output (MIMO) radar has gradually become a research hotspot due to its unique structural characteristics. By introducing a small frequency offset in the transmitting array, the echo signal contains phase characteristics related to distance. By analyzing the phase change caused by the frequency difference in the received signal, the joint angle-distance estimation of the target can be achieved, effectively improving the resolvability of multiple targets and the accuracy of parameter estimation.

[0003] In recent years, for the joint distance-angle estimation problem in frequency-controlled array MIMO radars, a variety of parameter estimation algorithms have been proposed, including the classical multiple signal classification (MUSIC), estimation of signal parameters via rotational invariance techniques (ESPRIT), approximate maximum likelihood estimation (AP-MLE), and methods based on tensor decomposition such as higher-order singular value decomposition (HOSVD) and parallel factor (PARAFAC) decomposition. These methods have shown good performance in achieving high-resolution estimation of target parameters. However, existing methods generally rely on ideal or pre-calibrated array structures and do not effectively consider the unknown mutual coupling effects existing in the radar antenna array. In frequency-controlled array MIMO radars, array mutual coupling will cause pattern distortion, thus significantly reducing the accuracy of target parameter estimation.

[0004] Currently, existing research has focused on the problem of unknown mutual coupling effects in the frequency diverse array (FDA) MIMO radar array. In the paper by J. Zhu, S. Zhu, J. Xu, and L. Lan (Adaptive Detectors for FDA-MIMO Radar With Unknown Mutual Coupling [J]. IEEE Signal Process. Lett., vol. 30, pp. 1437-1441, 2023.), the adaptive target detection problem of FDA-MIMO radar under array mutual coupling was studied. However, it did not estimate the angle and distance of the target. In the paper by L. Liu, H. Zhang, L. Lan, and J.-Y. Deng (Joint Range and Angle Estimation by FDA-MIMO Radar With Unknown Mutual Coupling[J]. IEEE Trans. Aerosp. Electron. Syst., vol. 59, no. 4, pp. 3669-3683, 2023.), a target parameter estimation algorithm for FDA-MIMO radar based on the MUSIC algorithm was proposed, which can effectively eliminate the influence of array mutual coupling and achieve joint estimation of direction of arrival (DOA)-distance. However, this method does not fully utilize the multi-dimensional structure of the received signal, and the spectral peak search brings a high computational complexity. At the same time, existing methods often need to assume that the number of targets is known, which increases the limitations in practical applications. Summary of the Invention

[0005] Object of the Invention: Aiming at the defects of the existing technology, the present invention proposes a parameter estimation method for FDA-MIMO radar based on Bayesian tensors. This method fully exploits the multi-dimensional structural characteristics of the received signal through tensor modeling, effectively suppresses the influence of array mutual coupling with the help of a selection matrix, and realizes high-precision target parameter estimation using Bayesian tensor decomposition under the condition that the number of targets is known or unknown.

[0006] Technical Solution: The parameter estimation method for FDA-MIMO radar based on Bayesian tensors described in the present invention includes:

[0007] Construct a third-order complex-valued tensor model for the received signal of the FDA-MIMO radar containing unknown mutual coupling, DOA, and distance information;

[0008] Design a selection matrix using the properties of array mutual coupling to eliminate the influence of array mutual coupling in the third-order complex-valued tensor received signal;

[0009] Optimize the tensor model through real-valued and compression operations to obtain a third-order real-valued compressed tensor, so as to reduce the computational complexity of tensor decomposition;

[0010] Use Bayesian tensor decomposition to estimate three factor matrices, and then obtain the target number, DOA, and distance information;

[0011] Furthermore, construct the received signal of the frequency-controlled array MIMO radar containing unknown mutual coupling, DOA, and distance information into a third-order complex-valued tensor model, specifically including:

[0012] In a monostatic frequency-controlled array MIMO radar, both the transmitting and receiving arrays are uniform linear arrays, which are composed of and array elements respectively. Due to the existence of frequency increment in the transmitting array, the carrier frequency of the th transmitting array element is , where is the initial carrier frequency of the frequency-controlled array MIMO radar. Considering the influence of unknown mutual coupling on the transmitting and receiving arrays, use and to represent the unknown mutual coupling matrices of the transmitting and receiving arrays respectively, where represents a Toeplitz matrix, and represent the unknown mutual coupling coefficients of the th transmitting and receiving array elements and satisfy and , represents the complex number field. Assume that the frequency-controlled array MIMO radar contains pulses within a coherent processing interval and simultaneously detects incoherent targets, then the DOA and distance of the th target are respectively represented as and . The received signal after matched filtering under the influence of array mutual coupling and at the th pulse can be expressed as:

[0013]

[0014] where and represent the transmitting and receiving steering matrices affected by array mutual coupling, and respectively represent the transmitting and receiving steering matrices in the ideal state, and respectively represent the and th column vectors of , Denote the signal feature matrix containing the target radar cross-section reflection coefficient and Doppler frequency shift, Denote the matrix transpose operation, Denote the diagonal matrix composed of the th row elements, Denote the Gaussian noise matrix with a mean of 0 and a variance of .

[0015] Utilize , where Denote the matrix vectorization operation, and then stack along the pulse dimension for times to obtain the received signal , that is,

[0016]

[0017] where, Denote the Khatri-Rao product, is the noise matrix. Further, can be regarded as the matrix expansion form of the PARAFAC model , that is,

[0018]

[0019] where Denote the third-order identity tensor, Denote the -mode matrix product of the tensor, , is the noise tensor.

[0020] Furthermore, utilize the property of array mutual coupling to design a selection matrix to eliminate the influence of array mutual coupling in the received signal of the third-order complex-valued tensor, specifically including:

[0021] Utilize and matrix properties to construct the selection matrices and , which can eliminate the unknown mutual coupling influence in , where and respectively denote all-zero matrices with dimensions of and , and respectively denote identity matrices with dimensions of and , and , and then obtain the third-order tensor , that is,

[0022]

[0023] where and represent the transmit and receive steering matrices after eliminating the unknown mutual coupling, and their column vectors, i.e., and are respectively composed of the first and rows of and rows of elements. In addition, represents the product of matrix and matrix , and the diagonal matrix satisfies , where represents the Hadamard product, , , and represent scaling factors, represents the diagonalization operation, and is the noise tensor.

[0024] Furthermore, the tensor model is optimized through the real-valued and compression operations to obtain a third-order real-valued compressed tensor to reduce the computational complexity of tensor decomposition, specifically including:

[0025] Since , where represents the conjugate operation, and the column vectors of matrices and are respectively the central Hermitian vectors composed of the column vector elements corresponding to and . is a diagonal matrix containing DOA and distance information. Combining with the conjugate tensor of tensor , i.e., , a new tensor is

[0026]

[0027] where represents the product of matrices , , and , is the transformed noise tensor, represents a permutation matrix with subdiagonal elements of 1 and the remaining elements of 0 and dimension size , and the subscript is .

[0028] Using the property , the tensor is re-expressed as , where denotes the product of matrices , and . Therefore, through the forward and backward smoothing operations, the complex-valued central Hermitian tensor can be obtained, where represents the concatenation operation of two tensors in the third dimension.

[0029] Then, using the unitary transformation operation, is transformed into a third-order real-valued tensor , that is

[0030]

[0031] where , and are three real-valued factor matrices, denotes the matrix conjugate transpose operation, represents the matrix and stacked by rows, represents the real number field, is the noise tensor, denotes the unitary matrix, whose subscript is odd and satisfies , and when the subscript is even, it satisfies , that is

[0032]

[0033] where is a positive integer, is the imaginary unit, denotes the identity matrix with dimension size , represents the all-zero matrix, denotes the exchange matrix with dimension size and sub-diagonal elements equal to 1 and the rest of the elements equal to 0.

[0034] Based on the obtained real-valued tensor, using the approximate HOSVD technique, is compressed to obtain the real-valued compressed tensor , that is

[0035]

[0036] where , and are orthogonal matrices, which are respectively obtained from the third-order tensor The three mode matrices are unfolded and then subjected to singular value decomposition to obtain the first , and left singular value vectors. Vectorize , and utilize the properties of the Khatri-Rao product to obtain

[0037]

[0038] where, denotes the Kronecker product, , and represent the compressed real-valued factor matrices, and can be equivalently represented as:

[0039]

[0040] where is the compressed noise tensor.

[0041] Furthermore, Bayesian tensor decomposition is adopted to estimate the three factor matrices, and then the target number, DOA, and distance information are obtained. Specifically, it includes:

[0042] First, establish a tensor probability model and define the likelihood function of as

[0043]

[0044] where, denotes being proportional to the symbol, represents the exponential operation, represents the Frobenius norm, is the Kruskal operator, denotes the noise precision term, and its prior distribution is modeled as a gamma distribution with hyperparameters , that is

[0045]

[0046] where represents the gamma function.

[0047] The prior distribution of the factor matrix is modeled as a generalized hyperbolic distribution with a hierarchical structure, that is

[0048]

[0049] where, denotes the maximum rank of the tensor , denotes The column vector, represents a Gaussian distribution, represents a vector of all zeros with a dimension size of ; represents an identity matrix with a dimension size of ; represents and 's product. Additionally, represents a latent factor, which is modeled as a generalized inverse Gaussian distribution with hyperparameter , i.e.,

[0050]

[0051] where represents the modified Bessel function of the second kind.

[0052] Define the set of unknown parameters , calculate the joint distribution of and as

[0053]

[0054] Use Bayesian thinking to calculate the posterior distribution of as

[0055]

[0056] Since directly calculating is highly complex, variational Bayesian inference is used to find a posterior distribution such that the Kullback-Leibler (KL) divergence value between and is minimized, i.e.,

[0057]

[0058] where represents the KL divergence value between and , , represents the mathematical expectation under the distribution , is a constant.

[0059] Furthermore, the KL divergence minimization problem is transformed into a maximization problem of , i.e., .

[0060] Based on the mean field theory, i.e., , we can obtain Optimal solution is

[0061]

[0062] wherein, represents the mathematical expectation of the distribution of other variables in except . Furthermore, , and in their optimal forms, i.e., , and , are solved sequentially through . By iterating to reach the convergence threshold, the estimated value of is obtained, i.e., .

[0063] During the iteration process, the mean of the -1 power of the latent factor , i.e., , will be continuously updated. Due to the sparsity of the prior selection of the factor matrix , in values will prompt the corresponding in columns of elements to be 0. The tensor rank is obtained by enumerating the non-zero columns in each factor matrix, i.e., determining the target number .

[0064] After obtaining the real-valued factor matrix , it is first necessary to recover the complex-valued factor matrix , i.e.,

[0065]

[0066] Then, the phase containing parameter information is calculated from and , and the estimated value of is further solved , i.e.,

[0067]

[0068] wherein, and respectively represent and the th column vectors, represents the wavelength, represents the speed of light, is the adjacent array element spacing, and They are the sine and arcsine functions respectively.

[0069] Advantages: Compared with the prior art, its main advantages are as follows: The present invention can make full use of the multi-dimensional structure of the received signals of the frequency-controlled array MIMO radar by using tensor modeling. The influence of array mutual coupling can be effectively eliminated by designing and selecting matrices. The proposed Bayesian tensor decomposition method can achieve accurate DOA and distance estimation whether the number of targets is known or unknown. The advantages and methods of the present invention can be further understood through the following detailed description of the invention and the accompanying drawings. Description of the Drawings

[0070] Figure 1 It is a flowchart of a method for estimating the parameters of a frequency-controlled array MIMO radar based on Bayesian tensors according to the present invention;

[0071] Figure 2 It is a schematic structural diagram of a frequency-controlled array MIMO radar with array mutual coupling according to the present invention;

[0072] Figure 3 It is a performance graph of the relationship between the root mean square error (RMSE) of DOA estimation and the signal-to-noise ratio (SNR) of the present invention and the existing dimension-reduced MUSIC method, the existing ESPRIT method, and the existing unitary HOSVD method under the condition of known number of targets;

[0073] Figure 4 It is a performance graph of the relationship between the RMSE of distance estimation and the SNR of the present invention and the existing dimension-reduced MUSIC method, the existing ESPRIT method, and the existing unitary HOSVD method under the condition of known number of targets;

[0074] Figure 5 It is a performance graph of the relationship between the RMSE of DOA estimation and the SNR of the present invention under multiple different unknown numbers of targets and numbers of pulses;

[0075] Figure 6 It is a performance graph of the relationship between the RMSE of distance estimation and the SNR of the present invention under multiple different unknown numbers of targets and numbers of pulses. Detailed Embodiments

[0076] To make the features and advantages of the present invention more obvious and understandable, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0077] Figure 2 It is a schematic structural diagram of a frequency-controlled array MIMO radar under the condition of array mutual coupling according to the present invention. As Figure 2 shown, the frequency-controlled array MIMO radar array contains the number of transmitting array elements, the number of receiving array elements. There is an unknown mutual coupling problem between the transmitting array and the receiving array. Within the range of interest of the radar, there are For a target, the transmitting array transmits mutually orthogonal signals, and the DOA and distance of the target are extracted by analyzing the echo signals after matched filtering.

[0078] Implementation Example 1

[0079] Please refer to Figure 3 and Figure 4 , these two figures are the performance diagrams of the RMSE and SNR relationships of DOA and distance estimations for the known number of targets in the present invention, compared with the existing dimension-reduced MUSIC method, the existing ESPRIT method, and the existing unitary HOSVD method. The system parameters are: , , , , , , and the SNR varies from -10 dB to 20 dB at an interval of 5 dB. It can be found that the proposed method and the existing methods can effectively eliminate the influence of array mutual coupling in the frequency-controlled array MIMO radar, and the RMSE of DOA and distance estimations for the proposed method and the existing methods gradually decreases as the SNR increases. In addition, the DOA and distance estimation performance of the proposed method is always superior to that of the existing methods. This is because the proposed method uses tensor modeling, and higher-precision factor matrix estimation is obtained by using tensor real-valuedization and iterative-based Bayesian tensor decomposition operations, thus producing superior DOA and distance estimation performance in the presence of array mutual coupling in the frequency-controlled array MIMO radar.

[0080] Implementation Example 2

[0081] Please refer to Figure 5 and Figure 6 , these two figures are the performance diagrams of the RMSE and SNR relationships of DOA and distance estimations for different numbers of unknown targets and pulses in the present invention. Considering , , , , , , and the SNR varies from -10 dB to 20 dB at an interval of 5 dB. They show that the proposed method can accurately estimate the DOA and distance of the target under different numbers of unknown targets , thus relaxing the prior requirement of the known number of targets. Although increasing the number of unknown targets will increase the difficulty of the proposed method to achieve accurate parameter estimation, the estimation accuracy of DOA and distance can be effectively improved by increasing the number of pulses . This shows that the proposed method can adapt to the actual scenario applications with multiple unknown numbers of targets.

[0082] In summary, the present invention contemplates a method for estimating the parameters of a frequency-controlled array MIMO radar based on Bayesian tensors. By tensor modeling, the multi-dimensional structure of the received signal can be fully utilized, and the influence of array mutual coupling can be effectively eliminated by using a selection matrix. Based on the proposed Bayesian tensor decomposition method, high-precision estimation of the DOA and distance of the target can be achieved whether the number of targets is known or unknown.

[0083] The description of the above embodiments is only to help understand the method and its main idea of the present invention. The content of this specification cannot be used to limit the scope of the rights of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims

1. A method for parameter estimation of a frequency-controlled array MIMO radar based on Bayesian tensors, characterized in that The method includes: Constructing the received signals of a frequency-controlled array MIMO radar containing unknown mutual coupling, DOA, and distance information into a third-order complex-valued tensor model; Designing a selection matrix using the properties of array mutual coupling to eliminate the influence of array mutual coupling in the third-order complex-valued tensor received signals; Optimizing the tensor model through real-valued and compression operations to obtain a third-order real-valued compressed tensor, so as to reduce the computational complexity of tensor decomposition; Adopting Bayesian tensor decomposition to estimate three factor matrices, and further obtaining the number of targets, DOA, and distance information.

2. A method for parameter estimation of a frequency-controlled array MIMO radar based on Bayesian tensors according to claim 1, characterized in that Construct the received signal of the frequency-controlled array MIMO radar containing unknown mutual coupling, DOA, and distance information into a third-order complex-valued tensor model, specifically including: Consider a monostatic frequency-controlled array MIMO radar affected by array mutual coupling. The transmitting array and the receiving array respectively contain and array elements, both of which are uniform linear arrays. The number of targets is , and the DOA and distance of the th target are respectively represented as and . The unknown mutual coupling matrices of the transmitting and receiving arrays are and respectively, where represents a Toeplitz matrix, and are respectively the unknown mutual coupling coefficients of the th transmitting array element and receiving array element, and , represents the complex number field. There is a frequency increment between the transmitting array elements of the frequency-controlled array MIMO radar. The carrier frequency of the th transmitting array element is , where is the initial carrier frequency. The frequency-controlled array MIMO radar has pulses within a coherent processing interval. Then, the received signal after matched filtering under the influence of array mutual coupling and at the th pulse is ， Among them, and represent the transmitting and receiving steering matrices affected by array mutual coupling, , , and respectively represent the and th column vectors of the matrix, represents the signal feature matrix containing the target radar cross-section reflection coefficient and Doppler frequency shift, represents the matrix transpose operation, is represented by th diagonal matrix formed by the row elements, represents a Gaussian noise matrix with a mean of 0 and a variance of . Vectorizing results in , where represents the matrix vectorization operation. Let be stacked along the pulse dimension times to obtain , which satisfies the matrix expansion form of the tensor , and is ， Among them, represents a third-order identity tensor, represents the -mode matrix product of the tensor, , is a noise tensor.

3. A method for parameter estimation of a frequency control array MIMO radar based on Bayesian tensors according to claim 1, characterized in that Design a selection matrix using the properties of array mutual coupling to eliminate the influence of array mutual coupling in the received signal of a third-order complex-valued tensor, specifically including: using the transmitting and receiving array mutual coupling matrices and to construct the selection matrices and to eliminate the unknown mutual coupling influence in , where and respectively represent all-zero matrices with dimensions of and , and respectively represent identity matrices with dimensions of and , and , and then obtain the third-order tensor as ， Among them and represent the transmit and receive steering matrices after eliminating array mutual coupling. The th column vectors, namely and , are respectively composed of the first and rows of and . represents the product of matrix and matrix . The diagonal matrix satisfies , where represents the Hadamard product, , , and represent scaling factors, represents the diagonalization operation, is the noise tensor.

4. A method for estimating parameters of a frequency-controlled array MIMO radar based on Bayesian tensors according to claim 1, characterized in that, Optimize the tensor model through real-valued and compression operations to obtain a third-order real-valued compressed tensor, so as to reduce the computational complexity of tensor decomposition, specifically including: using the property and the conjugate tensor of tensor , that is , to obtain a new tensor which is ， Among them, denotes the Khatri-Rao product, denotes the conjugate operation, and The column vectors of and respectively form the central Hermitian vector composed of the corresponding column vector elements. denotes the matrix , , and product of is a diagonal matrix containing DOA and distance information, is the transformed noise tensor, denotes a permutation matrix with subdiagonal elements of size equal to 1 and the remaining elements equal to 0, subscript . In addition, using the property the tensor is re-expressed as ， Among them represents the matrix 、 and The product of, through the front and back smoothing operations, a complex-valued central Hermitian tensor is obtained, where represents the concatenation operation of two tensors in the third dimension. Using the unitary transformation operation, is transformed into a third-order real-valued tensor That is ， Among them, , and are three real-valued factor matrices, represents the matrix conjugate transpose operation, represents the matrix and 's row stacking result, represents the real number field, is the noise tensor, represents a unitary matrix, whose subscript is odd and satisfies , and when the subscript is even, it satisfies , that is ， where is a positive integer, is the imaginary unit, represents the identity matrix with dimension size , represents the all-zero matrix, represents the exchange matrix with the subdiagonal being 1 and the remaining elements being 0 and having dimension size . Further, using the approximate HOSVD technique to compress to obtain the real-valued compressed tensor , that is ， Among them , and are orthogonal matrices, which are respectively obtained by performing singular value decomposition on the expansions of the three mode matrices of the third-order tensor and taking the first , and left singular value vectors. Vectorize and obtain by using the property of the Khatri-Rao product ， Among them, represents the Kronecker product, , and represent the compressed real-valued factor matrices, and thus is represented as: ， Among them is the compressed noise tensor.

5. A method for parameter estimation of a frequency-controlled array MIMO radar based on Bayesian tensors according to claim 1, characterized in that, Estimate three factor matrices by Bayesian tensor decomposition, and then obtain the target number, DOA, and distance information, specifically including: First, establish a tensor probability model and define The likelihood function of is ， Among them, represents the proportional symbol, represents the exponentiation operation, represents the Frobenius norm, is the Kruskal operator, represents the noise precision term, whose prior distribution is modeled as a gamma distribution with hyperparameter i.e., ， where denotes the gamma function, and the prior distribution of the factor matrix is modeled as a generalized hyperbolic distribution with a hierarchical structure, i.e., ， Among them, represents the maximum rank of the tensor , represents the th column vector of represents a Gaussian distribution represents a vector of all zeros with a dimension size of , represents an identity matrix with a dimension size of , represents and the product of represents a latent factor, which is modeled as a generalized inverse Gaussian distribution with hyperparameters i.e., ， Among them, represents the second kind of Bessel function, and defines the set of unknown parameters , calculate and The joint distribution of is ， Calculate using Bayesian thinking The posterior distribution of ， Furthermore, variational Bayesian inference is used to find a posterior distribution , such that and the Kullback-Leibler (KL) divergence value between them is minimized, that is ， Among them, denotes the KL divergence value between and which represents the mathematical expectation under the distribution is a constant. Then, the KL divergence minimization problem is transformed into a maximization problem of that is, based on the mean field theory, namely we obtain the optimal solution of as ， Among them, represents the mathematical expectation of the distribution of other variables in except . Furthermore, , and in the optimal form, that is, , and . Then, by solving them in sequence and reaching the convergence threshold through iteration to solve the estimated value, that is, . During the iteration process, the mean of the -1 power of the latent factor , that is, , will be continuously updated. Due to the sparsity of the prior selection of the factor matrix , in values prompt the corresponding column elements in to be 0. The tensor rank is obtained by enumerating the non-zero columns in each factor matrix, that is, determining the target number . After obtaining the real-valued factor matrix and , first, the complex-valued factor matrices and need to be recovered, and then the phase containing parameter information is obtained from , that is, ， Among them, and respectively represent and the th column vectors, represents the wavelength, represents the speed of light, is the adjacent element spacing, and are the sine and arcsine functions respectively.

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